61. The refracting angle of a prism is ’ A ’, and refractive index of the material of the prism is cot(A/2). The angle of minimum deviation is :

61. The refracting angle of a prism is ’ A ’, and refractive index of the material of the prism is cot(A/2). The angle of minimum deviation is :

(a) 180° − 2 A

(b) 90° − A

(c) 180° + 2 A

(d) 180° − 3 A

Answer :  (a) 180° − 2 A

\(\frac{\sin i}{\sin r} = \mu = \cot \frac{A}{2}\)

\(\frac{\sin \frac{\delta_{min}+A}{2}}{\sin \frac{A}{2}} = \frac{\cos \frac{A}{2}}{\sin \frac{A}{2}}\)

\(\sin \frac{\delta_{min}+A}{2} = \sin \left(90^\circ - \frac{A}{2}\right)\)

\(\frac{\delta_{min}+A}{2} = 90^\circ - \frac{A}{2}\)

\(\delta_{min} = 180^\circ - 2A\)